Kahler-Einstein metrics and volume minimization

Kahler-Einstein metrics and volume minimization

November 16, 2016 - 03:00
- November 16, 2016 - 04:00

Chi Li, Purdue University

Fine Hall 314

Futaki invariant is an obstruction to the existence of Kahler-Einstein metrics on Fano manifolds. Martelli-Sparks-Yau showed that the Futaki invariant is the derivative of a normalized volume functional on the space of Reeb vector fields of associated affine cones and derived the volume minimization principle for more general Sasaki-Einstein metrics. I will show that this volume minimization principle can be extended to work on a much bigger space of centered real valuations. This gives an equivalent characterization of K-semistability (which is equivalent to ``almost Kahler-Einstein”) and has an interesting algebra-geometric consequence. If time permits, I will also discuss the generalization to the case of Sasaki-Einstein metrics and some relation to metric tangent cones on singular Kahler-Einstein varieties. This talk is partly based on joint works with Yuchen Liu and Chenyang Xu.